Basis graphs of greedoids and two-connectivity

Pivoting, i.e. exchanging exactly one element in a basis, is a fundamental step in the simplex algorithm for linear programming. This operation has a combinatorial analogue in matroids and greedoids. In this paper we study pivoting for bases of greedoids. We show that for 2-connected greedoids any basis can be obtained from any other by a (finite) sequence of pivots.